3) Develop matrix form of the quadratic spline polynorhials for these data po: (1, 1), (2, 3), (3, 5), (4, 2).

Q: FIND THE FUNDAMENTAL MATRIX AS WELL AS THE FUND AMENTAR MATRIX ø (6)= I %3D SATISEYING x' = 2 -5 -2

A: Fundamental matrix is formed with linearly independent solution sets of the system. These linearly…

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4. A = -4 -3 L U

A: We have to find L and U matrix.

Q: Compute the product 0 () 0 (²) as a 2 x 2 matrix. What kind of isometry is this product?

A: Given product is  Oπ5O2π15 where Oθ represents rotation matrix through an angle θ in anti-clockwise…

Q: The output matrix is X: (Round HooimaL

A:

Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Create a matrix A with the given Characteristics Dimension 3x3, IAl = 7 %3D

A: Here we create a 3×3 matrix whose determinants is zero.

Q: a) Form the product PD and interpret its entries. b) Prediction of this population distribution…

A: The population dynamic is represented as D=0.80.20.30.7 and the population matrix is P=0.50.5. a)…

Q: Find an LU-factorization of the matrix A such that A = LU. %3D 6 4 -2 1 -2 3 2. -2

A: Explanation of the answer is as follows

Q: Find a matrix P that diagonalizes A

A:

Q: Show that when performing LU decomposition of an nxn element matrix for a set of linear equations,…

A: L U decomposition of a matrix is the factorization of a given square matrix into two triangular…

Q: What scaling matrix S (in homogeneous coordinates, so 3 by 3) would produce a 1 by 1 square page…

A:

Q: Choose all models with orthogonal design: Model with the design matrix -1 -1 -1 0 with x1 = (-1.9…

A: Model is orthogonal if  1. XXT=I Where, X = matrix  XT=transponse of matrixI = Identity matrix 2.…

Q: why cant we just multiply the 1/det(A) with the transpose of matrix like indicated in the red…

A: I am attaching image so that you understand each and every step.

Q: I, explain why BTB must be symmetric for any n × m matrix B. (If yo

A: We will prove that the matrix Is symmetric as following.

Q: ГО 5 4 5 1 2 2 3] A = [1

A:

Q: How can I find a matrix, given the basis of the null space of said matrix?

A:

Q: Show that any matrix of size 3 by 3, can be written as the sum of two invertible matrices, that is,…

A:

Q: Is the matrix A = [] diagmalızable? Exploin %3D

A:

Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…

A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…

Q: If the rows of an n X n matrix A are linearly inde­pendent as vectors in Rn, what is the rank of A?…

A:

Q: If there is conformability what are the dimensions of the product matrix?

A: let's matrix A and matrix B has dimension as  m×n and n×p respectively then dimension of matrix…

Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

A:

Q: Is there any 2x2 matrix with all non-zero entries, that is not diagonalizable but invertible? If…

A: Solution

Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

A:

Q: Find Jordan form of this matrix

A:

Q: Find an upper triangular matrix that satisties 307 0.

A:

Q: A 3x4 matrix A has Rank 1, then dim NUTLA %3D

A: The rank nullity theorem says that if T is a linear transformation form a vector Space V to vector…

Q: suppose A be any Hew of have symmetric matoir order and this matrix 4x4 rank of 3 the caleulata the…

A:

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.

A:

Q: Suppose A is anmxn matrix whose columns are linearly independent. What is the nullity of A?

A:

Q: If the null space of a 7 × 6 matrix  is 5-dimensional, what is the dimension of the column space of…

A:

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: How do you determine the sensitivity for each non zero parameter in this leslie matrix model

A: To determine sensitivity of 2x2 matrix. Let, the 2x2 matrix be a b c d Here,  True positive…

Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of…

A: We solve given problem with the help of rank nullity theorem

Q: The size of the matrix X'Y, where X is a design matrix of size (k+1) by (k+1) and Y is the vector of…

A: The size of design matrix X is given by (k + 1) by (k + 1)  And Y is the vector of values of…

Q: If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the row space of A?

A:

Q: Find a (2x2) singular matrix A that maps (2, 2) into (1, 2).

A: Here in this question find a 2×2 matrix that maps (2,2)  into (1,2). Here i attached solution of…

Q: Explain why the row vectors of a 4 × 3 matrix form a linearly dependent set. (Assume all matrix…

A: Given: The Matrix is 4 * 3 matrix

Q: [2 3 find the invers of matrix A by using the elementary row operation, where A = 5.

A: For finding the inverse of any matrix A, at first we augment it with an identity matrix on the…

Q: Either the row vectors or the column vectors of a square matrix are linearly independent. True False

A: Any row vectors or column vectors of a square are said to be linearly independent if…

Q: What is the rank of a 7x9 matrix whose null space is five dimensional? rank A =

A:

Q: Find the LU composition of 1 | - matrix A =

A:

Q: If A is a matrix in Rmxn with {()} -5 C(A) = span 2 %3D -2 what is m?

A: If A is a matrix in R^(m×n) then A is a linear transformation form n to m

Q: Determine the REF and RREF of the given matrix. pls show complete solutions

A:

Q: If A is a skew-symmetric matrix then show that AAT = AT A and A² is symmetric. [Note AT denotes the…

A: We will use definition

Q: Suppose an image is saved as a matrix with a Singular Value Decomposition: A = USVT. Let the vector…

A: Suppose an image is saved as a matrix with a Singular Value Decomposition: A = USVT. Let the vectors…